## 4 Discussion  
One important factor in the simulation of electron scattering in specimens is the total and differential scattering cross-section. The ratio between \(\sigma_{inel}\) and \(\sigma_{el}\) varied in the literature. It was predicted to be \(\sim\)26/Z [17] or \(\sim\)20/Z [10; 28], which is about 3.25 or 2.5 for oxygen in amorphous ice. Based on the theoretical calculation and the data from ICRU Report 90 published in 2016, Drs. [PERSON], [PERSON], and [PERSON] [33] estimated the ratio was 4.1 and 5.3 for carbon at 300 KeV and 3 MeV, respectively. The higher the ratio, the more electrons experienced inelastic scattering and the narrower the electron trajectories and the beam radius. As a starting point, the ratio of 3 was chosen in this simulation.  
As proposed by [PERSON] et al. [10] and [PERSON] et al. [19], when focusing the electrons in the middle of the specimen, the geometric broadening was only 50% of that when electrons were focused on the top surface of the specimen. However, in the simulation, focusing on the middle of the specimen does not help to reduce the beam radius. This may be due to the fact that as soon as electrons enter the specimen, scattering starts, and electrons cannot be focused as in a vacuum. Thus, the beam radius in this simulation was 27.9 nm, about four times larger than that proposed by [PERSON] et al. [19] (a factor of two due to that focusing at the middle of the specimen does not reduce beam size, and another factor of two due to that multiple scattering effect becomes more significant for a 10-m-thick specimen).  
However, focusing on the middle of the specimen may benefit the STEM images, as the STEM images are formed by scanning the specimen from one spot to another spot. When electrons are focused on the top surface of the specimen, the beam profile is cone-shaped (i.e., beam radius increases as the depth increases). The formed STEM image does not cover the entire 3D slab (with void space between scanning spots in the top portion of the specimen). When electrons are focused on the middle or even the bottom of the specimen, the beam profile is cylinder-shaped, and the formed STEM image includes information from the entire 3D slab. Thus, it provides more complete and accurate information of the specimen.  
[PERSON] designed and coded the MC simulation program in Matlab and carried out the MC simulations. [PERSON] generated the electron profile and carried out the MC simulations. All authors collectively contributed to the writing of the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was partially funded by the DOE Office of Biological and Environmental Research grant number KP1607011, and the BNL LDRD grant number 22-029.  
The data presented in this study are available on request from the corresponding author.  
We would like to thank [PERSON] for her valuable insights and discussions on using STEM for imaging biological samples and [PERSON], [PERSON], and [PERSON] for their enlightening discussions on electron scattering in specimens.  
Figure 7: Effect of imaging modes on beam width at a depth of 5 μm (**A**) and 10 μm (**B**).  
Conflicts of Interest: The authors declare no competing financial and non-financial interests in relation to the work described in the paper.