## 1 Introduction  
Understanding the building blocks of living organisms is critical for advancing fields such as medicine, biochemistry, and material science. One way to study these structures is by observing them in three dimensions (3D) with nanoscale resolution, a process that requires advanced imaging techniques. Such high-resolution imaging enables researchers to understand cell behavior and its implications for environmental studies, health, energy, and other fields.  
While exciting imaging techniques such as single particle cryogenic electron microscopy (cryo-EM) allow researchers to determine the structure of biological macromolecules, the rapidly advancing technologies of volume electron microscopy (vEM) are being used to visualize 3D volumes with nanoscale resolution [1; 2]: serial block-face scanning electron microscopy (SBF-SEM) [3], focused ion beam scanning electron microscopy (FIB-SEM) [4], array tomography [5], cryo-FIB SEM [6; 7; 8; 9; 10], and cryo-electron tomography (cryo-ET) [11]. Despite the impressive discoveries made with vEM, it is fundamentally constrained by sample thickness. This limitation arises from the low penetration depth of the imaging electrons and the extensive time required for thinning the samples to achieve nanometer resolution. To visualize thick samples up to 10 \(\upmu\)m with nanometer resolution, mega-electron-volt scanning transmission electron microscopy (MeV-STEM) has been proposed [12]. STEM combines SEM and TEM techniques by directly focusing the electron beam on the sample like SEM but creating an image from transmitted electrons computationally. STEM has already demonstrated the ability to adequately image samples up to 1 \(\upmu\)m [13; 14], which is a significant improvement over cryo-EM. In STEM, image resolution depends on electron probe broadening and intensity, both measured by the number of electrons captured within a collection angle. Single and multiple elastic and inelastic scattering events with varying beam focal depth and collection angles have been previously investigated [15], revealing that increased sample thickness leads to greater beam widening and multiple scattering. However, simulations demonstrated that through a 10 \(\upmu\)m thick sample of amorphous ice, 42% of MeV electrons were collected within 10 mrad, confirming the viability of MeV-STEM. These simulations utilize the Monte Carlo (MC) technique, which uses random sampling with weighted probabilities to address complex systems that are difficult to solve analytically.  
To quantitatively model the interactions between high-energy electrons and various materials and systematically investigate the possibility and performance of MeV-STEM over materials other than amorphous ice, we carried out extensive MC simulations. In this study, a previously developed MC program was employed to study the effect of sample material, beam convergence semi-angle (angular spread of beam on incidence), collection angle, and beam energy. The beam width increases from amorphous ice to carbon, silicon dioxide, and crystalline silicon. The beam profiles are also significantly affected by the beam focusing position. The applicability of the Beer-Lambert law in predicting signal attenuation in MeV-STEM versus lower energy incident electrons is also investigated. The results further suggest that MeV-STEM is a promising technique for producing high-resolution images of thicker biological samples, capable of increasing the rate and scope of scientific discovery.