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Start date: 2023 × Type: Article × Subject: correlation analysis × WGL Institute: IPHT ×

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    Evaluating arbitrary strain configurations and doping in graphene with Raman spectroscopy
    (Bristol : IOP Publ., 2017-11-6) Mueller, Niclas S.; Heeg, Sebastian; Peña Alvarez, Miriam; Kusch, Patryk; Wasserroth, Sören; Clark, Nick; Schedin, Fredrik; Parthenios, John; Papagelis, Konstantinos; Galiotis, Costas; Kalbáč, Martin; Vijayaraghavan, Aravind; Huebner, Uwe; Gorbachev, Roman; Frank, Otakar; Reich, Stephanie
    The properties of graphene depend sensitively on strain and doping affecting its behavior in devices and allowing an advanced tailoring of this material. A knowledge of the strain configuration, i.e. the relative magnitude of the components of the strain tensor, is particularly crucial, because it governs effects like band-gap opening, pseudo-magnetic fields, and induced superconductivity. It also enters critically in the analysis of the doping level. We propose a method for evaluating unknown strain configurations and simultaneous doping in graphene using Raman spectroscopy. In our analysis we first extract the bare peak shift of the G and 2D modes by eliminating their splitting due to shear strain. The shifts from hydrostatic strain and doping are separated by a correlation analysis of the 2D and G frequencies, where we find Delta omega(2D)/Delta omega(G) = 2.21 +/- 0.05 for pure hydrostatic strain. We obtain the local hydrostatic strain, shear strain and doping without any assumption on the strain configuration prior to the analysis, as we demonstrate for two model cases: Graphene under uniaxial stress and graphene suspended on nanostructures that induce strain. Raman scattering with circular corotating polarization is ideal for analyzing frequency shifts, especially for weak strain when the peak splitting by shear strain cannot be resolved.
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    Correcting systematic errors by hybrid 2D correlation loss functions in nonlinear inverse modelling
    (San Francisco, California, US : PLOS, 2023) Mayerhöfer, Thomas G.; Noda, Isao; Pahlow, Susanne; Heintzmann, Rainer; Popp, Jürgen
    Recently a new family of loss functions called smart error sums has been suggested. These loss functions account for correlations within experimental data and force modeled data to obey these correlations. As a result, multiplicative systematic errors of experimental data can be revealed and corrected. The smart error sums are based on 2D correlation analysis which is a comparably recent methodology for analyzing spectroscopic data that has found broad application. In this contribution we mathematically generalize and break down this methodology and the smart error sums to uncover the mathematic roots and simplify it to craft a general tool beyond spectroscopic modelling. This reduction also allows a simplified discussion about limits and prospects of this new method including one of its potential future uses as a sophisticated loss function in deep learning. To support its deployment, the work includes computer code to allow reproduction of the basic results.