A Simulation of Electron Scattering in Metals and its Application for Scanning Electron Microscopy

Abstract

In a recent research, the scanning electron microscope(SEM) has been shown to provide spatial resolution of less than 0.5nm. With the knowledge of the ultimate resolution or the factor which controls the resolution, it is possible to optimize the specimen preparation method and the choice of various electron beam parameters (eg. acceleration voltage etc.) For a precise discussion of the SEM image, it is necessary to take into account not only the signal (electron) production and the propagation in a specimen and its emission from the surface, but also electron trajectories in vacuum toward the detector. However, electron scattering process in the specimen does not depend on the detection system, and the resolution is mainly attributed to the spatial distribution of the electron emission from the specimen surface. Here, we focused on the electron scattering mechanisms in metals and developed a Monte Carlo simulation model of electron trajectories. Also, this simulation is applied to evaluate a compositional contrast in the SEM.In the present study electron interactions with atomic potential, inner-shell electrons, conduction electrons are taken into account. Cross sections calculated by the present model are shown in Fig.1 for [l]elastic scattering, [2]inner-shell (1s, 2s, 2p for Al) electron ionization, [3]conduction electron ionization through non-radiative plasmon decay, and [4] stable plasmon excitation in the conduction band electrons for Al. For the elastic scattering, the Mott cross section is used. For inner-shell electron ionizations by an electron collision, the Gryzinski equation is used. In order to express the plasmon-electron interaction in a free electron gas at the conduction band, the Lindhard treatment is used. This treatment is based on the random phase approximation in the dielectric response function of metals. The cross section is shown in a unit of the inverse mean free path. The cross sections for conduction electron ionization and the plasmon excitation agree with the data of Tung, Ashley, and Ritchie. Cross sections for inner-shell electron ionization, which Tung et al. have derived using the generalized oscillator strength, are also shown in Fig.1 for a comparison.