Investigating the potential variation of in-operando semiconductor nanostructures in electron beam direction

BIO Web of Conferences 129, 04020 (2024) EMC 2024 https://doi.org/10.1051/bioconf/202412904020 Investigating the potential variation of in-operando semiconductor nanostructures in electron beam direction Hüseyin Çelik1, Mr. Robert Fuchs2, Dr. Dirk Berger3, Dr. Christian M. Günther3, Mr. Simon Gaebel4, Dr. Tolga Wagner5, Prof. Dr. Michael Lehmann1 1Technische Universität Berlin, Institute of Optics and Atomic Physics, Germany, 2Technische Universität Berlin, Institute of Theoretical Physics, Germany, 3Technische Universität Berlin, Center for Electron Microscopy (ZELMI), Germany, 4Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, Germany, 5Humboldt-Universität zu Berlin, Department of Physics, Germany Off-axis electron holography is a well-established method for the investigation of projected potential distributions down to atomic spatial resolution. However, in the case of in-operando (electrical biasing) investigations of externally controlled semiconductor nanostructures, parasitic modulations of the electron wave occur due to long-range electrostatic stray fields [1]. In addition, a well-known problem is the alteration of the sample during preparation using a focused ion beam (e.g. ion implantation, surface amorphization or generation of conducting surfaces), which also severely influences the potential distribution within the sample [2]. Both effects have a particular impact in the direction of the electron beam as well, which makes a quantitative analysis particularly difficult. Standard approaches to resolve the entire potential distribution involve projective tilt series and their tomographic reconstruction [3], which entail a significant measurement effort (e.g. sample tracking or long-time stability) and instrumentational limitations (e.g. limited tilt angle (i.e. missing wedge), interior Radon transform or parallax displacement), in addition to extensive simulations (e.g. FEM or DEM), which are highly computationally intensive and require rarely given knowledge of the microscopic charge carrier distribution. Here, a simple and intuitive model (SIMP) for the approximation of such potential distributions inside and outside nanostructured FIB-prepared samples of a p-n junction, requiring a limited set of parameters, is presented. The model uses only independent convolutions of an initial potential distribution (e.g. analytic textbook models) with a Gaussian kernel (see attached figure), allowing the reconstruction of the entire potential distribution from only one measured projection (electron hologram). In addition, various contacted semiconductor nanostructure samples (TEMlamellae) are produced in a systematic approach using FIB under varying preparation parameters (i.e. currents and acceleration voltages of the ions) to evaluate the proposed model. © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (https://creativecommons.org/licenses/by/4.0/). BIO Web of Conferences 129, 04020 (2024) EMC 2024 https://doi.org/10.1051/bioconf/202412904020 In comparison with FEM-simulations, representing an established simulation method, it can be shown that the self-developed model is able to accurately approximate the 3D electrostatic potential distribution of various contacted TEM-samples, whereby the computational complexity can be significantly reduced with respect to FEM-simulations (i.e. ~1000x faster with ~1/1000th of the memory usage at ~5000x more nodes). An excellent agreement can likewise be observed in comparison with electron holographic and tomographic investigations considering experimental restrictions, revealing the real potential distribution in propagation direction of the electron beam. By this, a significant reduction of the required computational power as well as a drastically simplified measurement process is achieved, paving the way towards quantitative electron holographic investigation of electrically biased semiconductor nanostructures. In particular, the latter can in turn also be used to understand the exact effects of the FIB-preparation (e.g. implantation concentration or implantation depth) on the sample, thus leading to improved preparation strategies. Graphic: Keywords: Electron-Holography, Semiconductor-Nanostructures, 3D-PotentialDistribution, Surface-Effects, Computational-Optimization Reference: [1] S. Yazdi et. al., Ultramicroscopy 152, 10 (2015). [2] D. Cooper et. al., Journal of Microscopy 233, 102 (2009). [3] A. C. Twitchett-Harrison et. al., Nano Lett. 7, 2020 (2007). 2  (...truncated)