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Katharina Lorenz

Publications and source records attributed to Katharina Lorenz.

10 recordsLinked to original sources
arXiv2026

Numerical analysis for the Stokes problem with non-homogeneous Dirichlet boundary condition

The Stokes problem with non-homogeneous Dirichlet boundary condition is solved numerically using conforming discretizations and an approximation of the boundary datum in the corresponding trace space. Optimal discretization error estimates in various norms are derived. In the case of a homogeneous differential equation, all estimates of the velocity error are uniformly valid in the viscosity parameter for all conforming inf-sup stable discretizations. The theory accounts for the influence of corner singularities in the case of a non-convex domain. Several variants of the boundary data approximation are discussed. Moreover, the case of boundary data with very low regularity is studied, where a weak solution does not exist. The well-posedness of the very weak solution is investigated, and optimal discretization error estimates are derived. Numerical tests confirm the theory. The compatibility condition for the boundary data is not necessary for well-posedness of the weak and very weak formulations but it ensures that the solution satisfies the continuity equation in the distributional sense. In the same spirit, the compatibility condition is not necessary for the approximating boundary data; a good approximation of the original boundary data is important.

math.NA↗
arXiv2026

Formation of Ag and Au Plasmonic Nanoparticles by Ion Implantation in Ga$_2$O$_3$ thin films

Gallium oxide (Ga$_2$O$_3$) is a wide-bandgap semiconductor with exceptional electrical and optical properties, making it a promising material for optoelectronic and sensing applications. In this work, we demonstrate for the first time the formation of plasmonic silver (Ag) and gold (Au) nanoparticles embedded in Ga$_2$O$_3$ thin films via ion implantation. Ga$_2$O$_3$ films deposited by RF sputtering on sapphire substrates were implanted with Ag or Au ions at 150 keV and a nominal fluence of 5 $\times$ 10$^{16}$ ions/cm$^2$, followed by thermal annealing between 200 and 700 °C. Rutherford backscattering spectrometry (RBS) measurements revealed saturation effects during implantation, resulting in lower incorporated fluences, as well as out-diffusion with post-implantation annealing. Transmission electron microscopy confirmed the formation of metallic nanoparticles with a distribution consistent with the metal profiles measured by RBS. Optical absorption measurements showed a pronounced localized surface plasmon resonance (LSPR) band in the Ag-implanted films, visible even in the as-implanted state and red-shifting with increasing annealing temperature, while Au-implanted films exhibited a distinct LSPR peak only after annealing at $\geq$500 °C. The observed LSPR shifts with annealing are attributed primarily to changes in the Ga$_2$O$_3$ matrix rather than a change in nanoparticle size. These results establish ion implantation as a viable approach for integrating plasmonic nanostructures into Ga$_2$O$_3$.

cond-mat.mtrl-sci↗
arXiv2026

Au and Ag nanoparticles produced by ion implantation in single-crystalline $β$-Ga$_2$O$_3$

This work reports the successful formation of Ag and Au nanoparticles in $β$-Ga$_2$O$_3$ single-crystals by ion implantation and annealing at 550 °C. X-ray diffraction measurements revealed that nanoparticles were formed after the annealing step, presenting a highly-ordered crystalline structure and conforming to a crystallographic relation with respect to the matrix: $\left(0\overline{1}0\right)_β\parallel \left(110\right)_{\mathrm{Ag/Au}}$ and $\left[102\right]_β\parallel \left[1\overline{1}2\right]_{\mathrm{Ag/Au}}$. The presence of these nanoparticles was also confirmed via absorbance measurements revealing the localised surface plasmon resonance peaks associated with these particles. Considering the multiple advantages and the versatility of metallic nanoparticles, their combination with the exceptional properties of $β$-Ga$_2$O$_3$ paves the way for a wide range of applications.

cond-mat.mtrl-sci↗
arXiv2026

Anisotropic implantation damage build-up and crystal recovery in $β$-Ga$_2$O$_3$

The present work aims at investigating the defect accumulation and recovery dynamics in the inherently anisotropic $β$-Ga$_2$O$_3$ lattice. A systematic Rutherford Backscattering Spectrometry in Channelling mode (RBS/C) analysis of Cr-implanted samples was performed across multiple surface orientations and channelling directions. Distinct apparent defect accumulation and annealing rates were observed along different channelling axes, mainly attributed to the shadowing of certain types of defects along some directions. The efficient defect removal observed after annealing was correlated with the strain relaxation observed via High-Resolution X-ray diffraction (HRXRD) at temperatures as low as 500 °C, which is attributed to the removal of point defects. Annealing at higher temperature further improves crystalline quality but at a slower rate. In short, this work enhances the understanding of the effect of structural anisotropic properties of $β$-Ga$_2$O$_3$ during ion implantation, as well as the crystal recovery during thermal annealing, highlighting the interplay between crystallography and defect dynamics.

cond-mat.mtrl-sci↗
arXiv2026

Understanding the anisotropic response of $β$-Ga$_2$O$_3$ to ion implantation

While $β$-Ga$_2$O$_3$ is considered a promising wide bandgap semiconductor, the impact of ion-induced defect formation and anisotropic elasticity remains poorly understood. Here, we combine a simulation and experiment X-ray diffraction (XRD) study of the strain-stress dynamics induced by ion implantation into $β$-Ga$_2$O$_3$ single-crystals with different surface orientations. The strain accumulation in the out-of-plane direction is observed by XRD to occur in an anisotropic manner, with compressive strain along the [010] direction and tensile strain along the directions perpendicular to (100) and (001). An anisotropic stress/strain accumulation model is proposed and probed via Molecular Dynamics (MD), showing an excellent agreement with the experiments. For higher damage levels, pole figures obtained both experimentally and by MD via a novel reciprocal-space projection method reveal an orientation-independent $β$-to-$γ$ phase transition, with a fixed crystallographic relationship between the polymorphs. By exploring the strain-stress dynamics in anisotropic systems, this work establishes a method to directly compare macroscale diffraction experiments and atomistic simulations and opens a new path to engineer the properties of such systems utilizing their anisotropic response to ion implantation/irradiation.

cond-mat.mtrl-sci↗
arXiv2026

Study on the Effect of Annealing on Ga$_2$O$_3$ Thin Films Deposited on Silicon by RF Sputtering

Gallium oxide is an ultra-wide bandgap semiconductor with excellent opto-electronic properties, making it a highly promising material for a wide range of applications and devices. In this article, we report how the optical, morphological, structural, and compositional properties of $β$-Ga$_2$O$_3$ thin films deposited by RF sputtering on silicon substrates are affected by thermal treatments. Ellipsometric spectra recorded at multiple angles of incidence from several samples subjected to thermal annealing in the range of 550-1000 $^\circ$C were analyzed to extract the optical functions using appropriate multilayer models. This analysis is complemented by compositional, structural, and morphological characterization techniques. A significant increase of the refractive index was found after annealing at 1000 $^\circ$C, accompanied by a stark improvement in the samples' crystalline structure, as confirmed by complementary structural and compositional characterization techniques.

cond-mat.mtrl-sci↗
arXiv2025

UV photodetectors and field-effect transistors based on $β$-Ga$_2$O$_3$ nanomembranes produced by ion-beam-assisted exfoliation

$β$-Ga$_{2}$O$_{3}$ nanomembranes, obtained by ion-beam-assisted exfoliation, are used in the fabrication of simple metal-semiconductor-metal (MSM) structures, that are tested as photodetectors (PD) and field-effect transistors (FET). Ti/Au contacts to the membrane are found to be rectifying. However, through thermal treatment in a nitrogen atmosphere for one minute at 500 °C, it is possible to modify this junction to have an ohmic behavior. An MSM PD is studied, reaching a high responsivity of 2.6$\times$10$^{4}$ A/W and a detectivity of 2.4$\times$10$^{14}$ Jones, under 245 nm wavelength illumination, and an applied voltage of 40 V. In order to better understand the behavior of the two junctions, in particular the iono/photocurrent mechanisms, an ion microprobe system is used to assess the response of these PD when excitation is localized in the different regions of the device. Finally, a depletion-mode FET is obtained, with an on/off current ratio of 7.7$\times$10$^{7}$ in the linear regime, at a drain-to-source voltage of 5 V, and with a threshold voltage around $-$3 V. The success in obtaining FET, and most notably, MSM photodetectors, while using a simple device structure, indicates a great potential of the nanomembranes produced by ion-beam-assisted exfoliation for the development of high-performance devices.

cond-mat.mtrl-sci↗
arXiv2025

Effect of Annealing on Al Diffusion and its Impact on the Properties of Ga$_2$O$_3$ Thin Films Deposited on c-plane Sapphire by RF Sputtering

Gallium oxide is a wide-bandgap semiconductor which has been steadily growing in popularity due to its ultra-wide bandgap, suitability for harsh environments and distinctive opto-electrical properties. Notable applications include deep-UV photodetectors, low loss waveguides or even transparent solar cells. RF sputtering stands out among possible techniques for the epitaxial deposition of Ga$_{2}$O$_{3}$ thin films with high quality and at a low cost. By using sapphire substrates, and through thermal annealing, we can form a $β$-(Al$_{x}$Ga$_{1-x}$)$_{2}$O$_{3}$ alloy by Al diffusion, which has tunable opto-electrical properties such as the bandgap and breakdown electric field. In this work, techniques such as X-ray diffraction, Rutherford backscattering spectrometry, Raman spectroscopy, atomic force microscopy and optical transmission are used to determine the optical properties, morphology and composition of Ga$_{2}$O$_{3}$ deposited and annealed thin films. To explore the formation of the $β$-(Al$_{x}$Ga$_{1-x}$)$_{2}$O$_{3}$ alloy, annealing was performed at variable temperature, in ambient air. It was determined that the bandgap can indeed be tuned between 4.85 and 5.30 eV by varying the annealing temperature, corresponding to an Al content between 0$-$68.5.

cond-mat.mtrl-sci↗
arXiv2025

Microtubes and nanomembranes by ion-beam-induced exfoliation of $β$-Ga$_{2}$O$_{3}$

This paper reports an innovative process to fabricate $β$-Ga$_{2}$O$_{3}$ microtubes and nanomembranes based on ion implantation in (100)-oriented single-crystals. We show that, under specific flux and fluence conditions, the irradiation-induced strain profile promotes the detachment and rolling-up of a thin surface layer, forming a microtube. The strain-disorder interplay was investigated in detail for Cr-implanted $β$-Ga$_{2}$O$_{3}$ with a range of complementary methods, showing an excellent agreement between experimental and simulation data, and suggesting an exfoliation mechanism that is correlated with the anisotropic nature of the $β$-Ga$_{2}$O$_{3}$ monoclinic system and its easy-cleavage planes. Moreover, these microtubes can be unrolled upon a subsequent annealing step, resulting in nanomembranes with bulk-like crystalline quality that can be transferred to other substrates. The recovery of the implantation-induced damage under thermal annealing has also been studied, showing a remarkable recovery at moderate temperatures (~500 °C). This observation underscores the potential of this method for the scalable production of nanomembranes with improved reproducibility compared to conventional mechanical exfoliation techniques. Importantly, such exfoliation can be done employing different ions, providing simultaneous $β$-Ga$_{2}$O$_{3}$ doping, chosen to control the structural, optical, magnetic and electrical properties of the nanomembranes, thus tailoring them to fit the desired applications.

cond-mat.mtrl-sci↗