Towards an Accurate 3D Reconstruction of Nano-porous Structures using FIB Tomography and Monte Carlo Simulations with Machine Learning

Focused ion beam (FIB) tomography is a destructive imaging technique for collecting 3D structural information of micrometer sized samples at nanometer resolution. It requires a scanning electron microscope (SEM) with an additional FIB column. The SEM functionality is used for imaging serial-sections created with the focused ion beam. With state-of the art instruments, sample volumes of up to several thousand cubic micrometers can be imaged with a resolution of less than 5 nm in the imaging plane and as little as 5 nm in the slicing direction. Therefore, FIB tomography often serves as a 3D imaging method in between scanning transmission electron microscope (STEM) tomography (sample volumes of a few cubic micrometers at a resolution of about 1 nm) and X-ray nano-tomography (sample volumes of a few hundred cubic micrometers at a resolution of as little as 50 nm). Despite the high resolution, accurate reconstruction of nanostructures using FIB tomography data is challenging due to slicing and imaging artefacts, as well as intensity ambiguities in the SEM images (Figure 1). Segmentation of FIB tomography data is challenging, because high intensities do not necessarily represent structures at the FIB cross-section / imaging plane (turquois frame). Therefore, conventional segmentation algorithms will provide false structural information. Even though the second gold structure is brightest in the image (I2), the only gold at the surface of the serial cross-section is located at setup number four (I4). For the correct 3D reconstruction of porous systems, yet another main error source has to be considered: the shine-through effect [2]. This remains the case, even if the sample has been infiltrated before tomography, i.e., with epoxy resin. We developed a way to minimize FIB tomography artefacts, intensity ambiguities and shine-through effects by applying numerous strategies while acquiring the data as well as during data processing. Strategies for data acquisition include: a) adding rulers on the top and bottom sides of the samples for thickness knowledge of each individual FIB tomography section [3], and b) using multiple beam energies for backscatter electron (BSE) imaging of each slice. Strategies applied for data processing are: a) slice repositioning method, and b) in a supervised machine learning (ML) approach we are using Monte Carlo simulations to train the neural network for segmentation of real BSE image data of nano-structures and to improve results by integrating the multi-beam-energies into multimodal neural models [4]. On Monte Carlo-simulated BSE images of a virtual dataset of hierarchical nano-porous gold (HNPG) infiltrated with epoxy resin, where the number of voxels representing the structures and the resin is known (Figure 2), we achieved up to 18 times less false positive and false negative voxels using supervised ML with convolutional neural networks (CNN) in comparison to unsupervised ML segmentation with k-means (k=3). On real HNPG data, the reconstruction accuracy was measured for isotropic structures like HNPG with the two-point correlation function [4]. Here, we achieved an improvement of 20 - 30 % [5]. a) 2kV BSE image created using MCXray Monte Carlo simulation software [1]. The gray squares (I1 – I5) are gold cuboids in epoxy resin. Bar represents 50 nm. b) Schematic drawing of the gold cuboids setup underneath the imaging plane (d1-d5). Monte Carlo simulated BSE images at 1 to 4 kV of epoxy infiltrated HNPG (bar = 200 nm). Unsupervised ML segmentation (k-means, k=3) results are compared to supervised ML (CNN) results.