Mathematical modeling of the main characteristics of cold field and thermal field electron cathodes of scanning electron microscopes in the study of biological samples

Main emission characteristics of thermal field and cold field electron cathodes were calculated. Emitters surface forms are approximated by second-order surfaces and anodes are approximated by equipotential surfaces. Systems, consisting of 18 first order ordinary differential equations, are solved using the numerical Runge–Kutta method. As a result, trajectories of the “boundary” electrons were obtained, which determine beam shapes and sizes and density distributions charges and electric field strengths. Analysis of beam parameters let to determine special properties of scanning electron microscopes with thermal field electron cathodes and with cold field electron cathodes for studying biological samples.