A calculation approach for current density distribution evolution of secondary electrons using differential algebra method

In this study, the concept of the current density distribution (CDD) evolution of secondary electron (SE) beam is presented, and a novel approach using the differential algebra (DA) method is proposed to calculate the CDD evolution of the SE beam. Firstly, the emitted SE beam is divided into some beamlets in polar and azimuth angle directions. For each beamlet only one reference trajectory is traced using DA method. As a result, the transfer properties for this beamlet are obtained. Using the transfer properties, the current density function at arbitrary plane for the beamlet can be derived, in which the initial angle distribution, energy distribution and emission source size are considered. And then, the current density function is integrated, resulting in the CDD of this beamlet at arbitrary plane. Finally, the CDD evolution of the whole SE beam is obtained by superposing the CDDs of all beamlets. As an example, a SE detection system for a scanning electron microscope (SEM) is calculated using the proposed approach and therefore the SE CDD evolution is obtained and analyzed. Furthermore, experiments for observing the SE image of detector are performed, and the calculated SE CDD and the corresponding simulation images well explained the experimental results, validating the proposed calculation method. The proposed approach can be potentially applied for optimizing the SE detection system and therefore improving the collection efficiency of SE.