Numerische Methoden für innovative Halbleiter-Bauteile

Publikationen

Artikel in Referierten Journalen

• D. Abdel, M. Herda, M. Ziegler, C. Chainais-Hillairet, B. Spetzler, P. Farrell, Numerical analysis and simulation of lateral memristive devices: Schottky, ohmic, and multi-dimensional electrode models, Computers & Mathematics with Applications. An International Journal, 199 (2025), pp. 286--308, DOI 10.1016/j.camwa.2025.09.034 .
  Abstract
  In this paper, we present the numerical analysis and simulations of a multi-dimensional memristive device model. Memristive devices and memtransistors based on two-dimensional (2D) materials have demonstrated promising potential as components for next-generation artificial intelligence (AI) hardware and information technology. Our charge transport model describes the drift-diffusion of electrons, holes, and ionic defects self-consistently in an electric field. We incorporate two types of boundary models: ohmic and Schottky contacts. The coupled drift-diffusion partial differential equations are discretized using a physics-preserving Voronoi finite volume method. It relies on an implicit time-stepping scheme and the excess chemical potential flux approximation. We demonstrate that the fully discrete nonlinear scheme is unconditionally stable, preserving the free-energy structure of the continuous system and ensuring the non-negativity of carrier densities. Novel discrete entropy-dissipation inequalities for both boundary condition types in multiple dimensions allow us to prove the existence of discrete solutions. We perform multi-dimensional simulations to understand the impact of electrode configurations and device geometries, focusing on the hysteresis behavior in lateral 2D memristive devices. Three electrode configurations - side, top, and mixed contacts - are compared numerically for different geometries and boundary conditions. These simulations reveal the conditions under which a simplified one-dimensional electrode geometry can well represent the three electrode configurations. This work lays the foundations for developing accurate, efficient simulation tools for 2D memristive devices and memtransistors, offering tools and guidelines for their design and optimization in future applications.

• M. O'Donovan, R. Finn, P. Farrell, T. Streckenbach, J. Moatti, S. Schulz, Th. Koprucki, Developing a hybrid single band carrier transport model for (Al,Ga)N heterostructures, Journal of Computational Electronics, 24 (2025), pp. 114/1--114/19 (published online on 13.06.2025), DOI 10.1007/s10825-025-02333-2 .
  Abstract
  Aluminium gallium nitride (Al,Ga)N alloys and heterostructures are used in the development of UV light emitting devices, and can emit at energies extending into the UV-C spectral range. In the UV-C wavelength window and thus at high AlN content, devices exhibit poor quantum efciencies. In order to aid the development of these devices, simulation techniques which capture the essential physics of these materials and heterostructures should be used. Due to a change in band ordering in a quantum well at compositions close to Al0.75Ga0.25N, special attention should be given to the treatment of valence band states in device simulation. In this work we develop a hybrid single band efective mass model which is informed by degree of optical polarization data obtained from atomistic multi-band calculations. Overall, the hybrid single band efective mass model is benchmarked against tight-binding electronic structure calculations. To do so a confining energy landscape is extracted from the tight-binding model and used as input for the single band efective mass calculations. Moreover, the extracted tight-binding energy landscape is transferred to a drift-difusion model, allowing therefore for a multi-scale study of transport properties of a single (Al,Ga)N quantum well embedded in a p-i-n junction. Our results show that wider wells lead to a lower turn-on voltage due to a reduction of the band gap, but the internal quantum efciency of these wells is lower than in narrower wells. Alloy disorder leads to carrier localization and an uneven distribution of recombination within the quantum well plane, which gives rise to percolation currents. A comparison of results with 'pure' band simulations shows that when TE emission dominated, the heavy hole mass is a good approximation. In contrast, where band mixing was strong between heavy hole and split-of bands the mass from the split of band was very efective.

• C.L. Manganelli, D. Spirito, P. Farrell, J. Frigerio, A. De Lacovo, D. Marian, M. Virgilio, Strain engineering in semiconductor materials, physica status solidi (RLL) -- Rapid Research Letters (pss RRL), 19 (2025), pp. 2400383/1--2400383/3, DOI 10.1002/pssr.202400383 .
  Abstract
  Strain engineering has become an essential strategy in the advancement of semiconductor technologies, providing a power- ful mean to modulate the electronic, optical, and mechanical properties of materials. By introducing controlled deformation into crystal lattices, this approach enables enhanced carrier mobility, tailored bandgap energies, and improved device perfor- mance across applications in photonics, optoelectronics, and quantum technologies.

Beiträge zu Sammelwerken

• R. Finn, P. Farrell, T. Streckenbach, J. Moatti, S. Schulz, Th. Koprucki, M. O'Donovan, Multi-scale hybrid band simulation of (Al,Ga)N UV-C light emitting diodes, in: 25th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2025), IEEE, 2025, pp. 19--20, DOI 10.1109/NUSOD64393.2025.11199525 .
  Abstract
  Aluminium gallium nitride alloys are used for developing light emitting diodes operating in the UV part of the electromagnetic spectrum. These devices suffer from a low efficiency. To gain insight to this question we develop a 3-D modified drift-diffusion model which takes into account both alloy disorder effects and valence band mixing, and investigate the device efficiency. Results show that the current injection efficiency is strongly influenced by the chosen doping profile.

Preprints, Reports, Technical Reports

• G. Alì, Z. Amer, P. Farrell, N. Rotundo, Classical solutions for a van Roosbroeck--Helmholtz model for a semiconductor laser diode, Preprint no. 3228, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3228 .
  Abstract, PDF (365 kByte)
  We consider a coupled light-matter model for semiconductor lasers consisting of the transient van Roosbroeck system for charge transport and a Helmholtz eigenvalue problem for the transver- sal optical field. The coupling is realized through a stimulated recombination operator in the car- rier continuity equations and a carrier-dependent dielectric function in the Helmholtz problem. In this paper, we establish, under physically relevant assumptions, local-in-time well-posedness of the coupled van Roosbroeck--Helmholtz system. The proof relies on the abstract framework of quasi-linear parabolic equations in Banach spaces developed by Kaiser, Neidhardt, and Rehberg which requires in particular a local Lipschitz continuity property of the nonlinear recombination operators. By deriving precise local Lipschitz bounds for the stimulated recombination operator, we verify the conditions needed to apply the abstract existence theorem. As a consequence, we obtain the existence and uniqueness of weak solutions to a drift-diffusion-Helmholtz model of semiconductor lasers that incorporates stimulated emission in a mathematically consistent way. To the best of our knowledge, this is the first rigorous existence and uniqueness result for the nonlinear coupling of the van Roosbroeck system with a Helmholtz eigenvalue problem under physically motivated assumptions.

• Z. Amer, A. Avdzhieva, M. Bongarti, P. Dvurechensky, P. Farrell, U. Gotzes, F.M. Hante, A. Karsai, S. Kater, M. Landstorfer, M. Liero, D. Peschka, L. Plato, K. Spreckelsen, J. Taraz, B. Wagner, Modeling hydrogen embrittlement for pricing degradation in gas pipelines, Preprint no. 3201, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3201 .
  Abstract, PDF (12 MByte)
  This paper addresses aspects of the critical challenge of hydrogen embrittlement in the context of Germany's transition to a sustainable, hydrogen-inclusive energy system. As hydrogen infrastructure expands, estimating and pricing embrittlement become paramount due to safety, operational, and economic concerns. We present a twofold contribution: We discuss hydrogen embrittlement modeling using both continuum models and simplified approximations. Based on these models, we propose optimization-based pricing schemes for market makers, considering simplified cyclic loading and more complex digital twin models. Our approaches leverage widely-used subcritical crack growth models in steel pipelines, with parameters derived from experiments. The study highlights the challenges and potential solutions for incorporating hydrogen embrittlement into gas transportation planning and pricing, ultimately aiming to enhance the safety and economic viability of Germany's future energy infrastructure.

Vorträge, Poster

• D. Abdel, Charge transport in perovskite solar cells: Modelling, analysis and simulations, Workshop on Mathematical Models for Quantum and Semiclassical Dynamics, September 10 - 12, 2025, University of Florence, Department of Mathematics and Informatics Ülisse Dini", Italy, September 12, 2025.

• D. Abdel, Charge transport in perovskite solar cells: modelling, numerical analysis and simulations, Mini-workshop ARISE, Inria center at the University of Lille, Villeneuve d'Ascq, France, June 17, 2025.

• Z. Elsayed Amer, Modeling and simulation of a coupled van Roosbroeck--Helmholtz System, Workshop on Mathematical Models for Quantum and Semiclassical Dynamics, September 10 - 12, 2025, University of Florence, Department of Mathematics and Informatics Ülisse Dini", Italy, September 12, 2025.

• Z. Elsayed Amer, Numerical methods for a coupled drift-diffusion and Helmholtz model for laser applications, MESIGA25: Numerical Methods in Applied Mathematics, March 11 - 13, 2025, Institut für Mathematik der Universität Potsdam, March 12, 2025.

• Y. Hadjimichael, Strain distribution in zincblende and wurtzite nanowires bent by a one-sided stressor shell, Leibniz MMS Days 2025, March 26 - 28, 2025, The Leibniz Research Network "Mathematical Modeling and Simulation", Leibniz Institute for Baltic Sea Research Warnemünde (IOW), March 27, 2025.

• P. Farrell, Numerische Methoden für innovative Halbleiterbauteile, Transfer Workshop: ErUM-Scientists and Industry in Dialogue, February 6 - 7, 2025, ErUM Data Hub, Aachen, February 6, 2025.

• P. Farrell, Unravelling the mystery of enhanced open-circuit voltages in nanotextured perovskite solar cells, Kaiserslautern Applied and Industrial Mathematics Days - KLAIM 2025, October 6 - 8, 2025, Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM, Kaiserslautern, October 7, 2025.

Preprints im Fremdverlag

• D. Abdel, M. Herda, M. Ziegler, C. Chainais-Hillairet, B. Spetzler, P. Farrell, Numerical analysis and simulation of lateral memristive devices: Schottky, ohmic, and multi-dimensional electrode models, Preprint no. 15065, Cornell University, 2024, DOI 10.48550/arXiv.2412.15065 .
  Abstract
  In this paper, we present the numerical analysis and simulations of a multi-dimensional memristive device model. Memristive devices and memtransistors based on two-dimensional (2D) materials have demonstrated promising potential as components for next-generation artificial intelligence (AI) hardware and information technology. Our charge transport model describes the drift-diffusion of electrons, holes, and ionic defects self-consistently in an electric field. We incorporate two types of boundary models: ohmic and Schottky contacts. The coupled drift-diffusion partial differential equations are discretized using a physics-preserving Voronoi finite volume method. It relies on an implicit time-stepping scheme and the excess chemical potential flux approximation. We demonstrate that the fully discrete nonlinear scheme is unconditionally stable, preserving the free-energy structure of the continuous system and ensuring the non-negativity of carrier densities. Novel discrete entropy-dissipation inequalities for both boundary condition types in multiple dimensions allow us to prove the existence of discrete solutions. We perform multi-dimensional simulations to understand the impact of electrode configurations and device geometries, focusing on the hysteresis behavior in lateral 2D memristive devices. Three electrode configurations - side, top, and mixed contacts - are compared numerically for different geometries and boundary conditions. These simulations reveal the conditions under which a simplified one-dimensional electrode geometry can well represent the three electrode configurations. This work lays the foundations for developing accurate, efficient simulation tools for 2D memristive devices and memtransistors, offering tools and guidelines for their design and optimization in future applications.

• D. Abdel, J. Relle, Th. Kirchartz, P. Jaap, J. Fuhrmann, S. Burger, Ch. Becker, K. Jäger, P. Farrell, Unravelling the mystery of enhanced open-circuit voltages in nanotextured perovskite solar cells, Preprint no. 2506.10691, Cornell University, 2025, DOI 10.48550/arXiv.2506.10691 .
  Abstract
  Perovskite solar cells have reached power conversion efficiencies that rival those of established silicon photovoltaic technologies. Nanotextures in perovskite solar cells optimise light trapping and scattering, thereby improving optical absorption. In addition, nanotextures have been experimentally shown to enhance electronic performance, in particular, by increasing the open- circuit voltage VOC ? a phenomenon that, until now, has remained not fully understood. This study investigates the underlying reasons by combining multi-dimensional optical and charge- transport simulations for a single-junction perovskite solar cell. Our results reveal that the increased open-circuit voltage is not driven by optical effects but by the textured geometry itself. For voltages near VOC, texturing one of the absorber/transport layer interfaces increases the imbalance between electron and hole densities in the absorber, thereby reducing Shockley-Read- Hall (SRH) recombination, which is the dominant loss mechanism in this study. While idealised solar cells benefit unconditionally from increasing texture height, in realistic cells there is an optimal texture height which maximizes the power conversion efficiency. These findings provide new insights into the opto-electronic advantages of texturing and offer guidance for the design of next-generation textured perovskite-based solar cells, light emitting diodes, and photodetectors.

• B. Spetzler, E. Spetzler, S. Zamankhani, D. Abdel, P. Farrell, K.-U. Sattler, M. Ziegler, Physics-guided sequence modeling for fast simulation and design Exploration of 2D memristive devices, Preprint no. 2505.13882, Cornell University, 2025, DOI 10.48550/arXiv.2505.13882 .
  Abstract
  Modeling hysteretic switching dynamics in memristive devices is computationally demanding due to coupled ionic and electronic transport processes. This challenge is particularly relevant for emerging two-dimensional (2D) devices, which feature high-dimensional design spaces that remain largely unexplored. We introduce a physics-guided modeling framework that integrates high-fidelity finite-volume (FV) charge transport simulations with a long short-term memory (LSTM) artificial neural network (ANN) to predict dynamic current-voltage behavior. Trained on physically grounded simulation data, the ANN surrogate achieves more than four orders of magnitude speedup compared to the FV model, while maintaining direct access to physically meaningful input parameters and high accuracy with typical normalized errors <1%. This enables iterative tasks that were previously computationally prohibitive, including inverse modeling from experimental data, design space exploration via metric mapping and sensitivity analysis, as well as constrained multi-objective design optimization. Importantly, the framework preserves physical interpretability via access to detailed spatial dynamics, including carrier densities, vacancy distributions, and electrostatic potentials, through a direct link to the underlying FV model. Our approach establishes a scalable framework for efficient exploration, interpretation, and model-driven design of emerging 2D memristive and neuromorphic devices.