Figure 2

Electron interferometry with the two-grating structure. (a) GSM simulation of diffraction from the 20 μm interferometer. The black dashed lines represent imaging planes at different stage heights z, as explained in the text. In the interference plane, the two beams Ψ _0g (blue) and \({{\boldsymbol{\Psi }}}_{{\bf{g}}\bar{{\bf{g}}}}\) (dark green) overlap. (b) Magnified view of the region around the interference plane as indicated in (a). For a spatial coherence length equal to 20% of the beam diameter, the interference fringes extend for Δz ≈ 2.7 μm along the optical axis. The contrast seen in this image is caused by undersampling of the actual interference fringes, as explained in the text. (c) Magnified cross-section of the overlapping beams at the interference plane, as indicated in (b), showing fringes with the periodicity of the \([\bar{1}\bar{1}1]\) planes, 0.32 nm. (d) (z ₁ = 0) Ψ ₀ (center, pink circle), Ψ _g (right, light green circle) and \({{\boldsymbol{\Psi }}}_{\bar{{\bf{g}}}}\) (left) diffracted beams on the second grating. (z ₂ = −2 μm) Ψ _0g (circled in blue) separates out from Ψ ₀₀ (circled in yellow). \({{\boldsymbol{\Psi }}}_{{\bf{g}}\bar{{\bf{g}}}}\) is circled in dark green on the right. (z ₃ = −5.5 μm, z ₄ = −10.5 μm and z ₅ = −16 μm) Ψ _0g moves towards \({{\boldsymbol{\Psi }}}_{{\bf{g}}\bar{{\bf{g}}}}\). The measured distances between the beams are included in the text. (z ₆ = −20 μm) The two beams Ψ _0g and \({{\boldsymbol{\Psi }}}_{{\bf{g}}\bar{{\bf{g}}}}\) overlap and interfere. (e) TEM micrograph of the lattice of the second grating from the Ψ ₀ beam at z ₁ = 0. Inset shows the Fourier transform of the image, with multiple spots corresponding to the different lattice planes of silicon (110). (f) TEM micrograph of fringes from the interference of Ψ _0g and \({{\boldsymbol{\Psi }}}_{{\bf{g}}\bar{{\bf{g}}}}\) beams at z ₆ = −20 μm with a period 0.32 nm. The inset shows the Fourier transform of the image. Only one set of points (corresponding to g = \((\bar{1}\bar{1}1)\)) are seen around the central spot, confirming the origin of the fringes.