Wave Optical Modeling of the SEM Column From Source to Specimen

Probe formation in scanning electron microscope (SEM) is often reduced to objective lens action modeling based on a point-spread function or Fourier transforms. In this study, we present the first complete wave optical modeling of the whole SEM column based on plane-by-plane propagation of the electron beam wavefunction without simplifying the optical system. We identify the challenges in plane-by-plane beam propagation and show how sampling limitations produce aliased results. Through a careful selection and combination of propagators, we have developed a general wave optical propagation method that is able to overcome the aliasing problem to achieve the appropriate probe widths. Using a two-step propagator, we show that it is possible to model the electron beam distribution throughout the column from the virtual source plane to the specimen plane. We also show that our results from the wave optical simulations are consistent with the geometrical theory of probe formation. Finally, as a direct application of this method, we demonstrated that the combined effect of aberrations in the condenser lens and the probe forming objective lens cannot be accurately represented using only the objective lens. Designing beam shaping experiments and studying the effect of partial coherence can be some novel applications.