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.

在这项研究中，提出了二次电子（SE）束电流密度分布（CDD）演化的概念，并提出了一种使用微分代数（DA）方法来计算SE束CDD演化的新方法。首先，发射的SE光束在极角和方位角方向上被分成一些子束。对于每个子束，仅使用 DA 方法追踪一个参考轨迹。结果，获得了该子束的传输特性。利用传递特性，可以推导出子束在任意平面上的电流密度函数，其中考虑了初始角度分布、能量分布和发射源尺寸。然后，对电流密度函数进行积分，得到该子束在任意平面上的CDD。最后，通过叠加所有子束的 CDD 获得整个 SE 光束的 CDD 演化。例如，使用所提出的方法计算扫描电子显微镜 (SEM) 的 SE 检测系统，从而获得并分析 SE CDD 演化。此外，还进行了探测器SE图像观察实验，计算出的SE CDD和相应的仿真图像很好地解释了实验结果，验证了所提出的计算方法。所提出的方法可以潜在地应用于优化SE检测系统，从而提高SE的收集效率。