## 2 Methods
### MC Simulation  
The beam broadening in thick biological samples is governed by two effects: the geometrical beam divergence and the broadening due to plural scattering in the specimen. As discussed by [PERSON] et al. [19], the beam divergence angle was designed to be as small as 1 mrad. The corresponding beam profile was generated based on the recently demonstrated state-of-the-art 2 pm geometrical emittance, \(3\times 10^{-5}\) energy spread, and optimized chromatic (1.8 cm) and spherical (16 cm) aberrations of the STEM column [19]. An initial distribution with a total number of 10,000 electrons and the minimum root-mean-square (RMS) beam size of 1 nm and semi-convergence angle of 1 mrad at the focal position has been applied as the input file to MC simulations.  
In MC simulations, an electron was chosen from the electron profile randomly, then an event (elastically scattering, inelastic scattering, or no-scattering) was chosen based on the probability of each event in thickness \(dt\) as defined by Equations (3) and (5). However, the calculated ratio between \(\sigma_{inel}\) and \(\sigma_{el}\) (\(\sigma_{inel}/\sigma_{el}\)) is about 1.4, much lower than the theoretical  
Figure 1: Characteristic angle of elastic scattering (\(q_{0}\)) as a function of the beam energy.  
ratio (\(\sim\)26/Z) [17]. As pointed out by Dr. [PERSON] [32], the ratio is about 3 for 80-500 KeV electrons. Recently, Drs. [PERSON], [PERSON], and [PERSON] [33] showed that \(\sigma_{inel}/\sigma_{el}\) are 4.1 and 5.3 for carbon at 300 KeV and 3 MeV, respectively. Thus, the total inelastic scattering cross-section is scaled to be three times that of the total elastic scattering cross-section, \(\sigma_{inel}=3\sigma_{el}\) without considering the effect of high voltage on the ratio. The sample thickness \(dt\) was chosen to be 0.5 nm. Then, the scattering angle for elastic and inelastic scattering events was chosen based on the differential scattering cross-section for each angle interval \(d\theta\) based on Equations (2) and (4). For elastic scattering, the cross-section for each angle interval is the sum of the oxygen cross-section and two times the hydrogen cross-section. For inelastic scattering, the cross-section is 110% of the oxygen cross-section. The angle interval \(d\theta\) was set to 0.001 mrad for \(\theta\) smaller than 0.6 mrad, 0.01 mrad for \(\theta\) smaller than 6.3 mrad, 0.1 mrad for \(\theta\) smaller than 67 mrad, 1 mrad for \(\theta\) smaller than 600 mrad, and 10 mrad for other \(\theta\) angles. The position of the electron was updated based on the scattering angle and the distance \(dt\) along the scattering direction. Also, the event type was recorded. The procedure was repeated for 15 mm/\(dt\) = 30,000 times. As the scattering is circularly symmetric perpendicular to the incoming electrons, only a cross-section parallel to the incoming electrons was studied in the MC simulation.  
The beam size at depth \(t\) was calculated as the diameter of a disc containing 68% of the electrons reaching depth \(t\). Each electron at depth t was classified into the five groups discussed at the end of the previous section based on the events it experienced before reaching depth \(t\).