Atomic Resolution Tomography on Simulated Amorphous Silicon Nanoparticles

Electron microscopy images are inherently two-dimensional projections of three-dimensional objects. This difficulty has long been a focus in biology, resulting in the development of cryo-electron microscopy techniques, such as single-particle analysis for molecular structures [1], and cryo-tomography for analysis of larger-scale structures [2]. For parallel beam tomographic reconstructions, there is a requirement that the reconstructed object be monotonically related to the detected signal as an integral along the path of the incident radiation. In biological cryo-electron microscopy, the specimen is thin enough to be described as a weak phase object linearly related to the electron scattering potential [3]. In materials science, this criterion is met using a STEM probe with a high-angle annular dark-field (HAADF) detector [4]. However, for materials science, the ultimate goal of tomographic reconstruction is to focus on atom location and identification. Three-dimensional atomistic determination is a crucial advancement to describe defects, nucleation growth, and internal strain structures in materials science. The loss of information from the projection process results in an incomplete analysis of materials. However, a high confidence in the identification and determination process is required for detailed analysis of three-dimensional structures. The ultimate test for tomographic reconstruction is whether it is possible to correctly locate the position of every atom in an amorphous nanoparticle [5]. To investigate the feasibility, we determine the information, or the number of data points needed to locate all atoms in amorphous particles of different sizes (Fig. 1). We analyze, through a consideration of the power spectrum (Fig. 2), how the information available depends on signal/noise related to electron exposure and show that this limits particle size. Simulations on model Si nanostructures are used to investigate these limits by comparing the number of atoms found in the reconstruction with the number in the original model. This provides an ideal system with a known solution to describe the limitations of a single atom type reconstruction accurately and serves as a benchmark for experimental comparison. Reconstructed iso-surfaces of simulated amorphous nanoparticles with two degrees of electron counts: a) 25000 electrons per frame, and b) 10000 electrons per frame. Additionally, histograms of peak intensity values from the reconstructed volumes and 3D radial intensity values about each peak location (average+/-90%), are shown. The average radial profile of power spectra from micrographs was used to reconstruct the volumes represented in Fig 1. Horizontal lines correspond to power spectra peak values from images simulated with 25k electrons per frame(black) and 10k electrons per frame (red). These represent signals with the highest information transfer and exhibit an increase in information transfer with increasing electron counts.