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.