Correlating Optical Microspectroscopy with 4×4 Transfer Matrix Modeling for Characterizing Birefringent Van der Waals Materials - Schwarz, Julian; Niebauer, Michael; Kolesnik-Gray, Maria; Szabo, Maximilian; Baier, Leander; Chava, Phanish; Erbe, Artur; Krstic, Vojislav; Rommel, Mathias; Hutzler, Andreas (Small Methods, 2023)
Van der Waals materials exhibit intriguing properties for future electronic and optoelectronic devices. As those unique features strongly depend on the materials' thickness, it has to be accessed precisely for tailoring the performance of a specific device. In this study, a nondestructive and technologically easily implementable approach for accurate thickness determination of birefringent layered materials is introduced by combining optical reflectance measurements with a modular model comprising a 4×4 transfer matrix method and the optical components relevant to light microspectroscopy. This approach is demonstrated being reliable and precise for thickness determination of anisotropic materials like highly oriented pyrolytic graphite and black phosphorus in a range from atomic layers up to more than 100 nm. As a key feature, the method is well-suited even for encapsulated layers outperforming state of-the-art techniques like atomic force microscopy.
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Keywords: anisotropy; birefringence; microspectroscopy; thickness determination; transfer matrix method; van der Waals materials

Spectro-Spatial Unmixing in Optical Microspectroscopy for Thickness Determination of Layered Materials - Schwarz, Julian; Niebauer, Michael; Römling, Lukas; Pham, Adrian; Kolesnik-Gray, Maria; Evanschitzky, Peter; Vogel, Nicolas; Krstic, Vojislav; Rommel, Mathias; Hutzler, Andreas (Advanced Optical Materials, 2024)
Van der Waals materials and devices incorporating them exhibit highly thickness-dependent properties. The small lateral dimensions of mechanically exfoliated 2D-layered flakes, however, remarkably complicate their precise thickness determination. Quantitative analysis of reflectance measurements using optical microspectroscopy is proven to be as precise as spectroscopic ellipsometry while providing an easily adaptable and non-destructive method for thickness determination. The use of magnifying objective lenses allows obtaining the reflectance within a measurement spot of only a few microns in diameter. When the dimensions of exfoliated flakes are even smaller, however, the acquired reflectance is a superposition of those of the material of interest and the subjacent materials. To overcome this limitation, a facile approach to reduce the resolvable structure size by combining the evaluation of the reflectance measurement via transfer matrix method with spatial information extracted from optical micrographs is introduced. The efficacy when characterizing micrometer-sized flakes is exemplarily demonstrated for thickness determination of highly oriented pyrolytic graphite and a thin film of silicon dioxide. It is shown that a maximum error of less than 10% is achieved even when the flake only covers 20% of the measurement spot.
CRIS-Team Scopus Importer:2025-02-04
Keywords: 2D materials; graphite; reflectance; thin films; transfer matrix method

Unconventional conductivity increase in multilayer black phosphorus - Kolesnik-Gray, Maria; Meingast, Laura; Siebert, Martin; Unbehaun, Tim; Huf, Tobias; Ellrott, Günter; Abellan Saez, Gonzalo; Wild, Stefan; Lloret Segura, Vicente Josep; Mundloch, Udo; Schwarz, Julian; Niebauer, Michael; et al. (npj 2D Materials and Applications, 2023)
Multilayers of so-called 2D van der Waals materials have gained considerable attention as active components of next-generation electronic and optoelectronic technologies, with semiconducting black phosphorus (BP) regarded as one of the most promising systems. The applicability and performance limits of BP in both stand-alone and heterostructure-based multilayer devices are determined by individual flake charge transport properties, which synergistically depend on the number of layers and the strength of interlayer coupling between those. In this work, we study the DC electrical transport characteristics of high-quality BP field-effect devices within a wide range of flake thicknesses at room temperature. The experimental data show a non-trivial increase in conductivity and hole density with a reduced number of layers while maintaining constant field-effect mobility due to the prevalence of electron–phonon scattering. Based on the solution of the 1D Schrödinger–Poisson equation, we find that the observed phenomena are a direct consequence of non-negligible interlayer coupling, which in turn causes a local redistribution of free charge carriers towards the central layers. Our data show that due to the electrostatic conditions at the flake surfaces, a naturally protected 2D hole gas can be encapsulated in flakes as high as 10 nm, which preserves the bulk-like bandgap and effective carrier masses due to the electrostatic environment.
CRIS-Team Scopus Importer:2023-04-14