Electron Imaging Reconstruction for Pixelated Semiconductor Tracking Detectors in Transmission Electron Microscopes Using the Approach of Convolutional Neural Networks

Abstract

Energetic electrons of several hundred-kilo electron volts (keV) as used in transmission electron microscopy applications do not deposit their energy completely at their point of entry (PoE). Instead, in a detector with a thickness of 450 <inline-formula> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula>, they produce randomly 3-D tracks often extending over many pixels. The length and the shape of these tracks strongly depend on the primary energy of the electrons. Statistically, an electron deposits most of its energy at the end of its track. The output of a tracking detector system is the pixelated 2-D projection of the energy deposition. The proposed convolutional neural network (CNN) is capable of performing a frame-based event analysis and PoE reconstruction. The resulting modulation transfer function (MTF) is 0.77 at a Nyquist frequency of 0.5 obtained from a slanted edge. It is based on a U-net with a specially designed loss function using the confusion matrix. The input data to the CNN only need to be offset corrected. The output of the CNN is a PoE map containing the probability of a PoE of an electron for each pixel and frame. The architecture of the designed CNN also allows reconstructing different frame sizes without retraining the network.