Dynamic simulation of charging processes in polar dielectrics irradiated by the electron bunches of middle level energy

Nowadays the scanning electron microscopy techniques are widely used practically in condenser matter physics to study properties and structure of solids. The electron probe of scanning electron microscope is not merely a passive indicator of the geometrical or potential profile of the sample surface, but also the source producing ionizing, electric and thermal action on the sample. The application of raster electron methods to polar materials, responding to electric and heat exposures of the electron bunches allows us to get a response and create new modes of image formation. Let assume, that a sample surface of dielectric is irradiated by thin focused electron bunches of middle level energy (with order 1÷50 keV). When electrons bombard the dielectric sample the accumulation of absorbed electrons occurs. As a result generated charged areas can irregular drift the initial bunches. Charging effect occurs at any magnifications and any actual probe current. This work considers the results of dynamic simulation of charging process in polar dielectrics under the investigation with the scanning electron microscope. The purpose of present study is design and model implementation of three-dimensional dynamic model of charge relaxation in polar materials irradiated by electron bunches of middle level energy. The mathematical problem definition is given by the system of the continuity equation and Poisson equation. Final system of equations was modified in terms of intrinsic radiation-induced conductivity in sample as well as cylindrical symmetry of the problem. The simulation is based on numerical method solving of boundary problem for partial derivative equation system. In addition the initial electron distribution is determined by Monte-Carlo method using the programming implementation. To solve this problem we used the computational methods of solution of nonstationary mathematical physics problem such as finite difference method and finite element method realized with Matlab 7.0. The mathematical model of the charging process in ferroelectrics enables us to investigate the dynamics of charging process, and also to estimate the potential distribution at the given experimental parameters. (authors)