Direct Electron Detectors: Architecture and Algorithms

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Direct electron detectors (DED) are enabling new materials imaging techniques such as four-dimensional scanning transmission electron microscopy (4D-STEM)—and are now able to image biological specimens with higher resolution than x-rays. Limitations imposed by semiconductor manufacturing processes, where consumer electronics dominate device chip surface area, reduce the available space for DED pixels. To push beyond the physical pixel, sub-pixel super-resolution is necessary. I explore the prospects for sub-pixel super-resolution through electron counting as a function of diode depth, pixel pitch, and beam energy. For most energy ranges of interest to electron microscopy, energy is deposited as a string of charge across multiple pixels. I use machine learning to identify the start of the string, determining the true entry point of an electron with greater success than existing electron counting statistics. To test the effectiveness of different electron counters across beam energies and DED architectures, the electron counter is fed virtual detector readouts. Three electron counters are tested: the maximum intensity (peak) pixel; the center of mass (mean) point; and a convolutional neural network with a rectified linear unit (ReLU). I simulated primary beam energies from 30 to 5,000 keV for silicon and germanium diodes, with pixel pitches from 1 to 500 µm and diode depths from 10 to 1,000 µm. Electron paths are generated through an electron Monte Carlo method with relativistic corrections, then projected into a range of virtual detector pixels. The root mean squared error between the true entry point and the counter’s guessed entry point is used as a metric of performance. The simulations are performed, assuming a perfect signal with no additional noise, to test the maximum capability of counter performance. Super-resolution counting is effective up to 300 keV for a 500 µm diode, and up to 100 keV for shallower diode depth of 50 µm. The machine learning model has great performance with a training dataset of significantly smaller size than a typical 4D-STEM dataset. Similar trends for all counters are observed with respect to beam energy, pixel pitch, and diode depth. The electron counters are generally most dependent on diode depth for performance, followed by beam energy. There are three regions of dependencies on diode depth: a barreling region for backthinned diodes where the electron passes straight through; a peak error region where the electron path is cut off but given sufficient time to wander; and a region where the full point spread function is captured. By combining machine learning with a deep diode, a counting mode via integration is achieved.

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71 pages


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Detector; Electron; Imaging; Microscopy; Super-resolution


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Muller, David

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Benedek, Nicole
Bindel, David

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Materials Science and Engineering

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M.S., Materials Science and Engineering

Degree Level

Master of Science

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Government Document




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Attribution-ShareAlike 4.0 International


dissertation or thesis

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