THEORY OF ELECTRON-BEAM MOIRE

When a specimen surface carrying a high-frequency line grating is exam ined under a scanning electron microscope (SEM), moire fringes are obs erved at several different magnifications. The fringes are characteriz ed by their spatial frequency, orientation, and contrast. These featur es of the moire pattern depend on the spatial frequency mismatch betwe en the specimen grating and the raster scan lines, the diameter of the electron beam, and the detailed topography of the lines on the specim en. A mathematical model of e-beam moire is developed that expresses t he spatial dependence of the SEM image brightness as a product of the local intensity of the scanning beam and the local scattering function from the specimen grating. Equations are derived that give the spatia l frequency of the moire fringes as functions of the microscope settin gs and the spatial frequency of the specimen grating. The model also d escribes the contrast of several different types of moire fringes that are observed at different magnifications. We analyze the formation of these different fringe patterns, and divide them into different categ ories including natural fringes, fringes of multiplication, fringes of division, and fringes of rotation.