Electron beam charging of insulators: A self-consistent flight-drift model

Abstract

Electron beam irradiation and the self-consistent charge transport in bulk insulating samples are described by means of a new flight-drift model and an iterative computer simulation. Ballistic secondary electron and hole transport is followed by electron and hole drifts, their possible recombination and/or trapping in shallow and deep traps. The trap capture cross sections are the Poole-Frenkel-type temperature and field dependent. As a main result the spatial distributions of currents j(x,t), charges ρ(x,t), the field F(x,t), and the potential slope V(x,t) are obtained in a self-consistent procedure as well as the time-dependent secondary electron emission rate σ(t) and the surface potential V0(t). For bulk insulating samples the time-dependent distributions approach the final stationary state with j(x,t)=const=0 and σ=1. Especially for low electron beam energies E0<4keV the incorporation of mainly positive charges can be controlled by the potential VG of a vacuum grid in front of the target surface. For high beam energies E0=10, 20, and 30keV high negative surface potentials V0=−4, −14, and −24kV are obtained, respectively. Besides open nonconductive samples also positive ion-covered samples and targets with a conducting and grounded layer (metal or carbon) on the surface have been considered as used in environmental scanning electron microscopy and common SEM in order to prevent charging. Indeed, the potential distributions V(x) are considerably small in magnitude and do not affect the incident electron beam neither by retarding field effects in front of the surface nor within the bulk insulating sample. Thus the spatial scattering and excitation distributions are almost not affected.