Characterization of electron scattering in solids using a generalized walk

A new method to characterize electron scattering in solids is presented. This method is based on the concept of fractal geometry leading to a generalized walk. A criterion is presented to validate the applicability of this method. This method is applied to random walks with variable mean free path to validate it. Finally, this method is applied to the diffusion of incident electrons in solids of gold and carbon to characterize the transition between persistent and random walk processes describing the diffusion of the electrons in these materials.     

Monte Carlo modeling of secondary x-ray fluorescence across phase boundaries in electron probe microanalysis

Secondary fluorescence induced by photoelectric absorption of x-rays generated by an electron beam can occur when the characteristic x-ray energy of material “A” exceeds the critical excitation energy of material “B.” An expression is developed to calculate secondary fluorescence across a planar boundary from a discrete source placed at any (X, Y, Z) coordinates relative to the boundary. The expression can be incorporated into a Monte Carlo electron trajectory simulation which calculates the discrete distribution of primary x-ray generation.     

Simulations of scanning electron microscopy imaging and charging of insulating structures

We present a three‐dimensional simulation of scanning electron microscope (SEM) images and surface charging. First, the field above the sample is calculated using Laplace's equation with the proper boundary conditions; then, the simulation algorithm starts following the electron trajectory outside the sample by using electron ray tracing. When the electron collides with the specimen, the algorithm keeps track of the electron inside the sample by simulating the electron scattering history with a Monte Carlo code. During this phase, secondary and backscattered electrons are emitted to form an image and primary electrons are absorbed; therefore, a charge density is formed in the material. This charge density is used to recalculate the field above and inside the sample by solving the Poisson equation with the proper boundary conditions. Field equation, Monte Carlo scattering simulation, and electron ray tracing are therefore integrated in a self‐consistent fashion to form an algorithm capable of simulating charging and imaging of insulating structures. To maintain generality, this algorithm has been implemented in three dimensions. We shall apply the so‐defined simulation to calculate both the global surface voltage and local microfields induced by the scanning beam. Furthermore, we shall show how charging affects resolution and image formation in general and how its characteristics change when imaging parameters are changed. We shall address magnification, scanning strategy, and applied field. The results, compared with experiments, clearly indicate that charging and the proper boundary conditions must be included in order to simulate images of insulating features. Furthermore, we shall show that a three‐dimensional implementation is mandatory for understanding local field formation.