Abstract
A Patterson-like scheme is proposed for direct inversion of the conventional low energy electron diffraction (LEED) intensity versus energy I(E) curves, which is in contrast with the previously suggested holographic scheme. The surface sensitivity is guaranteed by using the fractional-order beams for inversion. Taking Si(113)-(3*2), Sb/Si(111) - (root3*root3)R30 and Si(111) - (7*7) surfaces as examples, we show that high-quality 3D atomic images can be obtained, by direct Patterson inversion of LEED-I(E) curves. While for the holographic inversion of LEED-I(E) curves, shifts (>1A) in z-coordinates of the atomic images are observed. As to the in-elastically scattered electrons (Kikuchi pattern), it is the holographic process that contributes to the intensity modulation of I(E) curves of the diffraction patterns, thus the holographic inversion has to be adopted to obtain the atomic images. Applying the off-normal Kikuchi electron holography (KEH) the controversial Si(113)-(3*2) surface, the capability of KEH to solve an unknown surface structure is demonstrated. The inverted atomic images reveal the characteristics of the puckering tetramer Ranke's model. Structural phase transitions of hydrogen passivated Si(113) surfaces were also studied by KEH.